Unless you have a camera with a remote control or cable release, the best option for taking your photo is to use the camera's self-timer. Many cameras have a two-second self-timer option for this very reason. This way you avoid any possibility of camera shake, and you can also make sure that your hands are not obstructing the lights.
If the object you are photographing doesn't fill the whole frame, then it's a good idea to make use of your camera's exposure compensation function and well. Shooting objects against a white background will tend to make the camera's automatic exposure system under-expose by a couple of stops, so set the exposure compensation to +1 or +2. See this tutorial for more information on exposure.
When you've taken your photo, you've probably got something that looks like the picture above. This is a good starting point, but we can improve it still further using an image editing program such as Adobe Photoshop or Corel Paint Shop Pro. The best tool to improve this picture, and indeed many digital images, is the Levels tool, which allows you to make fine adjustments to the relative brightness of different tones. In Photoshop (and in Photoshop Elements) you can find Levels using the keyboard shortcut CTRL + L, or in the menu under Image > Adjustments > Levels. In Paint Shop Pro it is in Adjust > Brightness & Contrast > Levels.
By moving the Input Level sliders to the positions shown in the picture above, I have changed the black point to enhance contrast, and made the entire background appear white. This really brings out the detail in the coin I have used as a subject, and also makes it a lot easier to cut out the background. All that remains is to crop the image down to remove the surplus white area, and we're done.